- 06-180 Christian Remling
- Discrete and embedded eigenvalues for one-dimensional Schr"odinger operators
Jun 12, 06
(auto. generated ps),
of related papers
Abstract. I present an example of a discrete Schr"odinger operator
that shows that it is possible to have embedded singular spectrum and, at the same time,
discrete eigenvalues that approach the edges of the essential spectrum (much) faster
than exponentially. This settles a conjecture of Simon (in the negative).
The potential is of von Neumann-Wigner type, with careful navigation around
a previously identified borderline situation.